Question

1. an apartment annual lease is 500 per month, but a person must stay the full year. a monthly lease is 600 per month. which equation helps find when the monthly lease is cheaper? o 500x = 6000 o 600x = 6000 o 600x = 7200 2) mike is going on a snowboarding vacation. renting a snowboard costs 30 dollars per day. buying costs 240 dollars, but the board can be resold to a used - goods store for 1/3rd the new price, so net cost is 240-(1/3)240 = 160. which equation helps find when buying is cheaper than renting? o 30 = 160x o 30x = 160 3) an individual movie ticket is 10 dollars. however, a theater club is 20 dollars per month for unlimited movies. how many movies must a person watch over a year for the clubs 20 x 12 or 240 dollar cost to be cheaper? o fewer than 24 o more than 24 4) ari likes a bands songs. online, each song individually costs 2 dollars. or, an album with 13 songs costs 15 dollars. at what number

Explanation:

1. Problem 1:

• Explanation:
• ## Step1: Set up the cost - comparison equation
• The annual lease cost is $500\times12 = 6000$ dollars. The monthly lease cost is $600$ dollars per month. Let $x$ be the number of months. We want to find when the monthly - lease cost is cheaper than the annual lease cost. So the equation is $600x<6000$.
• Answer: There is no correct option provided in the question for this part. The correct inequality should be $600x < 6000$.

1. Problem 2:

• Explanation:
• ## Step1: Calculate the new price
• The original price of the snow - board is $240$ dollars. It is sold at $\frac{1}{3}$ off. The discount amount is $\frac{1}{3}\times240 = 80$ dollars. The new price is $240−80 = 160$ dollars. If we let the new price be $x$, the equation to find $x$ is $240-( \frac{1}{3}\times240)=x$, or $240 - 80=x$. Among the given options, the correct equation is $240-(1/3)240 = 160$.
• Answer: $240-(1/3)240 = 160$

1. Problem 3:

• Explanation:
• ## Step1: Set up the cost - comparison equation
• The cost per month for the theater club is $20$ dollars. The cost per individual movie ticket is $10$ dollars. Let $x$ be the number of movies watched per month. The annual cost for the club is $20\times12$ dollars. We want to find when the cost of individual tickets is cheaper than the club cost over a year. The annual cost of individual tickets is $10x\times12$ dollars, and the club cost is $20\times12$ dollars. We want to find when $10x<20$.
• If we consider the cost per month, the equation to find when individual - ticket watching is cheaper is $10x<20$.
• Answer: There is no correct option provided in the question for this part. The correct inequality should be $10x < 20$.

1. Problem 4:

• Explanation:
• ## Step1: Set up the cost - comparison equation
• The cost of the album is $15$ dollars with $13$ songs. Each individual song costs $2$ dollars. Let $x$ be the number of songs. The cost of individual songs is $2x$ dollars. We want to find when the cost of individual songs is more than the album cost. So the equation is $2x>15$.
• To find the number of songs for which individual - song purchase is more expensive, we solve $2x>15$, $x > 7.5$. Since $x$ represents the number of songs, $x$ must be an integer, so $x\geq8$. And the number of songs for which individual - song purchase is more expensive is more than $7.5$, so more than $24$ is incorrect. Fewer than $24$ is also incorrect.
• If we consider the number of songs for which individual - song purchase is more expensive than the album, we set up the inequality $2x>15$, and $x>\frac{15}{2}=7.5$. Since $x$ is a non - negative integer, when $x = 8$, individual purchase is more expensive.
• Answer: There is no correct option provided in the question for this part. The correct inequality should be $2x>15$.

Answer:

1. Problem 1:

• Explanation:
• ## Step1: Set up the cost - comparison equation
• The annual lease cost is $500\times12 = 6000$ dollars. The monthly lease cost is $600$ dollars per month. Let $x$ be the number of months. We want to find when the monthly - lease cost is cheaper than the annual lease cost. So the equation is $600x<6000$.
• Answer: There is no correct option provided in the question for this part. The correct inequality should be $600x < 6000$.

1. Problem 2:

• Explanation:
• ## Step1: Calculate the new price
• The original price of the snow - board is $240$ dollars. It is sold at $\frac{1}{3}$ off. The discount amount is $\frac{1}{3}\times240 = 80$ dollars. The new price is $240−80 = 160$ dollars. If we let the new price be $x$, the equation to find $x$ is $240-( \frac{1}{3}\times240)=x$, or $240 - 80=x$. Among the given options, the correct equation is $240-(1/3)240 = 160$.
• Answer: $240-(1/3)240 = 160$

1. Problem 3:

• Explanation:
• ## Step1: Set up the cost - comparison equation
• The cost per month for the theater club is $20$ dollars. The cost per individual movie ticket is $10$ dollars. Let $x$ be the number of movies watched per month. The annual cost for the club is $20\times12$ dollars. We want to find when the cost of individual tickets is cheaper than the club cost over a year. The annual cost of individual tickets is $10x\times12$ dollars, and the club cost is $20\times12$ dollars. We want to find when $10x<20$.
• If we consider the cost per month, the equation to find when individual - ticket watching is cheaper is $10x<20$.
• Answer: There is no correct option provided in the question for this part. The correct inequality should be $10x < 20$.

1. Problem 4:

• Explanation:
• ## Step1: Set up the cost - comparison equation
• The cost of the album is $15$ dollars with $13$ songs. Each individual song costs $2$ dollars. Let $x$ be the number of songs. The cost of individual songs is $2x$ dollars. We want to find when the cost of individual songs is more than the album cost. So the equation is $2x>15$.
• To find the number of songs for which individual - song purchase is more expensive, we solve $2x>15$, $x > 7.5$. Since $x$ represents the number of songs, $x$ must be an integer, so $x\geq8$. And the number of songs for which individual - song purchase is more expensive is more than $7.5$, so more than $24$ is incorrect. Fewer than $24$ is also incorrect.
• If we consider the number of songs for which individual - song purchase is more expensive than the album, we set up the inequality $2x>15$, and $x>\frac{15}{2}=7.5$. Since $x$ is a non - negative integer, when $x = 8$, individual purchase is more expensive.
• Answer: There is no correct option provided in the question for this part. The correct inequality should be $2x>15$.